29.28.12 problem 810

Internal problem ID [5393]
Book : Ordinary differential equations and their solutions. By George Moseley Murphy. 1960
Section : Various 28
Problem number : 810
Date solved : Monday, January 27, 2025 at 11:17:58 AM
CAS classification : [_quadrature]

\begin{align*} {y^{\prime }}^{2}+\left (x +y\right ) y^{\prime }+y x&=0 \end{align*}

✓ Solution by Maple

Time used: 0.002 (sec). Leaf size: 20

dsolve(diff(y(x),x)^2+(x+y(x))*diff(y(x),x)+x*y(x) = 0,y(x), singsol=all)
 

\begin{align*} y \left (x \right ) &= -\frac {x^{2}}{2}+c_{1} \\ y \left (x \right ) &= {\mathrm e}^{-x} c_{1} \\ \end{align*}

✓ Solution by Mathematica

Time used: 0.036 (sec). Leaf size: 32

DSolve[(D[y[x],x])^2+(x+y[x])*D[y[x],x]+x*y[x]==0,y[x],x,IncludeSingularSolutions -> True]
 

\begin{align*} y(x)\to c_1 e^{-x} \\ y(x)\to -\frac {x^2}{2}+c_1 \\ y(x)\to 0 \\ \end{align*}